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Contractive idempotents on locally compact quantum groups
general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.
Classification of idempotent states on the compact quantum groups Uq(2), SUq(2), and SOq(3)
We give a simple characterisation of those idempotent states on compact quantum groups which arise as Haar states on quantum subgroups, show that all idempotent states on quantum groups Uq(2), SUq(2), and SOq(3) (q 2 (−1, 0) [ (0, 1]) arise in this manner and list the idempotent states on compact quantum semigroups U0(2), SU0(2), and SO0(3). In the Appendix we provide a simple proof of coamenability of the deformations of classical compact Lie groups.
Noncommutative topological entropy of endomorphisms of Cuntz algebras
Noncommutative topological entropy estimates are obtained for ‘finite range’ endomorphisms of Cuntz algebras, generalising known results for the canonical shift endomorphisms. Exact values are computed for a class of polynomial endomorphisms related to branching function systems introduced and studied by Bratteli, Jorgensen and Kawamura.